Freezing Swampland: A Krylov Complexity Criterion for the Weak Gravity Conjecture

This paper investigates the relationship between the Weak Gravity Conjecture (WGC) and quantum information theory, specifically focusing on whether the behavior of Krylov spread complexity can serve as a diagnostic for the stability of extremal black holes. The authors aim to determine if the approach to extremality in charged AdS black holes is encoded in the dynamics of the dual quantum state.

The researchers utilize the AdS/CFT correspondence to study a charged thermofield double state, which is holographically dual to an AdS Reissner–Nordström black hole. They employ Krylov complexity—a measure of how a quantum state spreads in the basis of Lanczos-constructed states—to analyze the system's dynamics. By calculating the cumulants of the grand-canonical Hamiltonian, they examine how the return amplitude and Krylov complexity behave as the black hole approaches the extremal limit. They further extend this framework by incorporating a charged scalar field to model the effect of Schwinger pair production, which acts as a discharge channel for the black hole.

The study demonstrates that as a black hole approaches the extremal limit, Krylov spreading effectively freezes; the return amplitude becomes a pure phase, and the spread complexity vanishes. This suggests that the extremal state is dynamically constrained in a way that prevents nontrivial evolution in Krylov space. However, when the authors introduce charged matter, the opening of a discharge channel via Schwinger pair production lifts this frozen behavior, restoring nontrivial dynamics. The authors propose that the absence of exact freezing in the presence of an available discharge channel provides a quantum-information-theoretic interpretation of the Weak Gravity Conjecture.

This work bridges the gap between the swampland program—which seeks to identify consistent theories of quantum gravity—and quantum information theory. By providing a dynamical, complexity-based diagnostic for the WGC, the paper suggests that fundamental constraints on gravity may be deeply rooted in the informational properties of quantum systems, offering a new perspective on black hole stability and the consistency of effective field theories.

AI-generated third-party summary by ResearchPod. Not official content or an endorsement by the paper authors or affiliated organizations.